Minimal and maximal extensions of M-hypoelliptic proper uniform pseudo-differential operators in $$L^p$$ -spaces on non-compact manifolds
Tóm tắt
In the context of manifolds of bounded geometry, we show that the properties of proper uniform pseudo-differential operators (PUPDOs) constructed by Kordyukov, Meladze, and Shubin carry over to PUPDOs whose local representations have symbols belonging to the (weighted) class
$$M_{\rho ,\varLambda }^{m}$$
introduced by Garello and Morando. Under the M-ellipticity assumption, we show that the minimal and maximal extensions of such PUPDOs in the
$$L^p$$
-spaces, where
$$1
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